Some Applications of the Lagrange Inversion Formula for the k-Fibonacci Numbers
Bakir Farhi
Laboratoire de Mathématiques Appliquées
Faculté des Sciences Exactes
Université de Bejaia
06000 Bejaia
Algeria
Abstract:
We provide summation formulas for the k-Fibonacci numbers (k ∈ Z, k ≥ 2) and their asymptotic equivalents in terms of generalized binomial
coefficients. Our main tools are the Lagrange inversion formula and one
of its consequences due to Hermite.
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(Concerned with sequences
A000045.)
Received September 28 2023; revised versions received September 30 2023; December 3 2023; December 21 2023; January 3 2024.
Published in Journal of Integer Sequences,
January 3 2024.
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